how to separate mesh with armature
I got it after few tries. Do as the following:


Select your object and goto Edit Mode.
Select vertices or faces you want to split.
Press P and select "By Selection".


The mesh messed up in my case is due to changing action after splitting mesh into 2 objects. Strangely, if you change action while selecting a 3D object, the mesh will go hay-wired. To solve that, be sure you select armature/bones when changing action.